In a vehicle powertrain, operating temperatures of an engine and a transmission are typically managed in part by a cooling system that has circulating coolant. An engine heat exchanger establishes thermal communication between engine oil and the coolant. A transmission heat exchanger establishes thermal communication between transmission fluid and the coolant. Coolant flow to the heat exchangers is typically via the same route whether in a cooling mode or in a heating mode. The heat exchangers must be sized to sufficiently perform the cooling and heating tasks.